{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-09-10T06:55:18.337029Z",
     "start_time": "2025-09-10T06:55:17.323807Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-10T06:55:18.342509Z",
     "start_time": "2025-09-10T06:55:18.339044Z"
    }
   },
   "cell_type": "code",
   "source": [
    "p = np.arange(0.01,1,0.01)\n",
    "H = -p * np.log2(p) - (1-p) * np.log2(1-p)\n"
   ],
   "id": "bda208c622540134",
   "outputs": [],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-10T06:55:18.459030Z",
     "start_time": "2025-09-10T06:55:18.343526Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(p,H)\n",
    "plt.show()"
   ],
   "id": "83bb56d20084927b",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 3
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
